This invention relates to projection imaging.
In such imaging, each raw data sample may (e.g., in the case of X-ray imaging) represent the attenuation of a beam projected through an object along one of many paths within a plane of interest. In other imaging schemes (e.g., positron emission), the data samples are derived from emissions originating at various locations within the object. In either case the data samples (which can generally be called projection samples) typically are mathematically processed by convolutional back projection to reconstruct a two-dimensional tomographic image of the plane of interest. Three-dimensional images can also be formed by back projection, but require a larger number of calculations.
In a second reconstruction technique, needing fewer calculations, a matrix of the projection samples is transformed from the real space domain to the frequency domain by Fourier transformation. The resulting Fourier transform values may be viewed as lying at specific locations on a complex plane. The Fourier transform values are used in an interpolation process that generates a corresponding set of values located at the intersection points of a rectilinear grid. An inverse Fourier transform then reconverts the grid values to a matrix of pixel values representing the desired image. Depending on the interpolation technique used, the image may exhibit distortion.